What are some common mistakes students make with Stefan's Law?

1 Answer

#1)# The body you consider must atleast approximate to a blackbody. Stefan's law holds only for black bodies.

#2)# If you are asked to experimentally verify Stefan's law using the torch bulb filament, be assured that you won't be able to obtain Stefan' law exactly from it. Power emitted will be proportional to #T^n# where #n# differs from #4#. So if you find out that #n# is #3.75#, you have done it right and you don't need to panic. (It is so primarily because a tungsten filament ain't a perfect blackbody).

#3)# Pay attention to the terms unit time and unit area. For a body with area A units, it has to be modified to #Q = sigma*A*T^4#. For a time #t#, multiply #Q# with #t#. However, most generally we deal with unit area and unit time. But, pay attention to the problem being asked.

#4)# As usual, pay attention to the units (whether they are all in the same system of units). Temperature is generally expressed in #K#.

#5)# The original Stefan's law states that power emitted by a perfect black body as radiation at temperature #T_1# per unit area, per unit time surrounded by another black body of temperature #T_2# is proportional to #(T_2)^4 - (T_1)^4#. But, when an external black body is absent, the expression reduces to #Q= sigma*T^4# where #T = T_1#.